1. Field of the Invention
The invention relates to an apparatus and method for measuring the ratio of the capacitance values of two capacitors having very small capacitances which have very small differences between them and are interconnected by means of one of their electrodes. Capacitances in the picofarad range and capacitance differences down to the femtofarad range are intended to be regarded as small.
2. Description of the Related Art
A circuit arrangement for measuring the quotient of the capacitance values of two capacitors which are to be compared with one another and are interconnected at one electrode is disclosed in DE 36 23 136 C2. The capacitors are interconnected on the signal output side. A DC signal is supplied via a switch to the free electrode of the one capacitor and is supplied via an operational amplifier and a further switch to the free electrode of the other capacitor. The two switches are connected in antiphase. Additionally connected in series with the operational amplifier is a further switch which opens delayed in time with respect to the other switches. During the time when this switch is open, currents flow from the two capacitors through the switch upstream of the operational amplifier. The mean current during this time is equal to zero. From this it results that the ratio of the input voltages of the capacitors is proportional to their capacitances.
Because of the use of the multiplicity of switches, the known method is problematic particularly for the measurement of very small capacitances. The control signals of the switches lead to small currents which are in the same order of magnitude as the currents flowing through the capacitances, and they are temperature-dependent. A disadvantage is also seen in that the assumption concerning the mean current is based on a time measurement.
The above-mentioned document discloses having pure voltage measurement at the output of the operational amplifier. The two capacitors are connected into the measurement circuit alternately. The frequency of the signal voltage can be selected to be up to the order of magnitude of 300 kHz and is limited by the response time of the analog switches. With a knowledge of the capacitance of one of the capacitors as a reference value, and measurement of the signal output values at the operational amplifier, it is intended to be possible to determine the other capacitance or its change in a sensitive manner. No statements are published on the lower limits of the measurable capacitances.
The measurement of capacitances in the picofarad range is necessary, for example for the characterization of integrated circuits using MOS or MIS technology. In this case, the capacitance must also be measured over a wide frequency range from a few Hertz to a few Megahertz. A suitable circuit arrangement is specified in EP 0,318,596 A1.
The equivalent circuit of an integrated circuit is a parallel circuit consisting of a capacitance and a resistance whose magnitude is not negligible. A DC voltage of variable amplitude and a superimposed AC voltage of variable frequency are applied to the component to measure the impedance. The AC voltage signal is preferably a triangular-wave signal. The output signal is converted into an AC signal via an operational amplifier with feedback. The top gradient and the amplitude of this AC signal are determined at a defined measurement time. The magnitude of the capacitance is then derived from the amplitude and that of the parallel resistance is derived from the top gradient. For absolute measurements, a known circuit can alternatively be inserted into the measurement arrangement as a reference.
It is not possible to measure the ratio of the capacitances of two unknown capacitors directly using this circuit.
The measurement principle of a number of sensors for inclination and/or acceleration indication is based on determining small capacitance changes in capacitor systems having very small capacitances. Such a sensor and a suitable evaluation circuit are described in DE-PS 2,523,446. The sensor comprises two electrode plates which are opposite one another at a fixed spacing between which a capacitor plate is located, suspended in a sprung manner.
The two electrode plates are connected to a generator for generating an AC voltage such that there are voltages of equal amplitude and frequency, but phase-shifted with respect to one another through 180.degree., on the electrode plates. The voltages acting on the capacitor plate thus counteract one another when the capacitor plate is located precisely between the electrode plates. If the capacitor plate deviates under the influence of gravity or inertia forces from its null position, an AC voltage is produced by the change in the capacitances between the electrode plates and the capacitor plate.
The capacitor plate is electrically connected to a measurement transducer in which this AC voltage is converted into a measurement signal for indicating the angle change in the position of the sensor. However, the AC voltage can also be supplied to a regulator which generates therefrom a regulated DC voltage signal which is superimposed on the AC voltage applied to the electrode plates. The regulator is configured such that the capacitor plate is held in its null position against the force acting on it. The angle change of the capacitor plate which is proportional to the inclination and/or acceleration can then likewise be determined from the DC voltage regulation signals.
The capacitance changes to be detected in the sensor are very small so that parasitic capacitances and leakage resistances of the connecting wires and other components of the printed-circuit board used for constructing the circuit have a critical effect on the accuracy and sensitivity. Regulation at the null position is very complex. Since the DC voltage used for returning the capacitor plate must be relatively high, there are additional insulation problems and particular requirements for the mechanical design of the sensor.